Ms. Davids became the Democratic nominee in the Third Congressional District in Kansas on Wednesday, according to The Associated Press. That sets her up against Representative Kevin Yoder, a Republican who has served since 2011.

She defeated five other Democratic candidates, including Brent Welder, who earned support and a campaign rally appearance from two stars of the progressive left, Senator Bernie Sanders and Alexandria Ocasio-Cortez, the Democratic nominee in New York’s 14th Congressional District.

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Representative Kevin Yoder of Kansas waved to supporters after winning the Republican primary in his district on Tuesday.CreditJohn Sleezer/The Kansas City Star, via Associated Press

Ms. Davids, a lawyer who spent a year as a White House fellow as President Barack Obama handed off to President Trump, campaigned on a conventional Democratic platform, including expanded health care access, gun control and opposition to Mr. Trump’s tax breaks.

A member of Ho-Chunk Nation, a Native American tribe in Wisconsin, Ms. Davids was backed by Emily’s List, a national organization dedicated to electing Democratic women.

Her campaign did not respond to a message on Wednesday, but in a statement she called Mr. Yoder “a pawn for Donald Trump.”

“Now, we turn to the general election and set our sights on defeating Kevin Yoder, an extremist who has tried time and time again to undermine health care access and give tax breaks for the largest corporations,” Ms. Davids said in the statement on Wednesday, according to The Kansas City Star.

Democrats believe they have a chance to pick up the seat, which represents the Kansas City area and its environs, as part of its larger quest to regain control of the House in the November general election. In a statement, Ben Ray Luján, the chairman of the Democratic Congressional Campaign Committee, called Ms. Davids “a strong voice for working families” who is “ready to bring that fight to Congress.”

“After this hard-fought primary win, Sharice emerges even stronger in her historic bid to flip this competitive seat,” he said.

“Having L.G.B.T. people sitting in the room while decisions are being made, and sitting there as peers, will shift the conversation,” she said. “I think it’s important that the lived experiences and the point of view of L.G.B.T. folks be included in conversations that affect all of us.”

While Ms. Davids would be the first congresswoman to have been an M.M.A. fighter, she would not be the first member of Congress with Octagon experience. Markwayne Mullin, a Republican from Oklahoma, is also a former M.M.A. fighter.